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J. Sib. Fed. Univ. Math. Phys., 2014, Volume 7, Issue 3, Pages 297–304 (Mi jsfu374)  

This article is cited in 4 scientific papers (total in 4 papers)

New periodic Gibbs measures for $q$-state Potts model on a Cayley tree

Rustamjon M. Khakimov

Institute of Mathematics, National University of Uzbekistan, Do’rmon Yo’li, 29, Tashkent, 100125, Uzbekistan

Abstract: In this paper under some conditions on parameters of the $q$-state Potts model on a Cayley tree of order k we prove existence of the periodic (non translation-invariant) Gibbs measures. Also we give a result about the number of such measures.

Keywords: Cayley tree, configuration, Potts model, Gibbs measure, periodic Gibbs measures, translation-invariant measures.

Full text: PDF file (162 kB)
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UDC: 517.98
Received: 06.03.2014
Received in revised form: 29.04.2014
Accepted: 26.05.2014
Language:

Citation: Rustamjon M. Khakimov, “New periodic Gibbs measures for $q$-state Potts model on a Cayley tree”, J. Sib. Fed. Univ. Math. Phys., 7:3 (2014), 297–304

Citation in format AMSBIB
\Bibitem{Kha14}
\by Rustamjon~M.~Khakimov
\paper New periodic Gibbs measures for $q$-state Potts model on a Cayley tree
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2014
\vol 7
\issue 3
\pages 297--304
\mathnet{http://mi.mathnet.ru/jsfu374}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. M. Khakimov, F. Kh. Khaidarov, “Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree”, Theoret. and Math. Phys., 189:2 (2016), 1651–1659  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. F. Haydarov, R. Khakimov, “An improvement of extremality regions for Gibbs measures of the Potts model on a Cayley tree”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, eds. S. Ayupov, V. Chilin, N. Ganikhodjaev, F. Mukhamedov, I. Rakhimov, IOP Publishing Ltd, 2016, 012019  crossref  isi  scopus
    3. U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 196:1 (2018), 1043–1058  mathnet  crossref  crossref  adsnasa  isi  elib
    4. R. M. Khakimov, M. T. Makhammadaliev, “Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 199:2 (2019), 726–735  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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